1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246
#![doc( html_logo_url = "https://raw.githubusercontent.com/owo-lang/voile-rs/master/rustdoc/icon.svg?sanitize=true" )] /* Documentation guidelines Formatting: + Less than 80 characters/line if possible (exceptions: for instant a link that is too long, where you can't cut it) + Use link-url separated markdown syntax + Colorize "TO DO"s Phrasing: + Only capitalize terms when used the first time + Name of programming languages should be capitalized (if needed) */ /*! Voile is a dependently-typed programming language evolved from [minitt]. # Design ## Goal The focus of Voile is *extensible algebraic data types* on top of *dependent types*. It can solve the expression problem without using any design patterns (like visitor or object-algebra in Java, or finally-tagless or DTALC in Haskell). We're pretty much inspired by the coexistence of guarded recursion, coinductive data types, sized types and inductive types in [Agda], which is nice to have all of them but they do not work very well as we can see in a discussion [here][agda-bad-bad] about guarded recursion checker or in [a GitHub issue][agda-bad] about the incompatibility between size and guarded recursion. We can observe that sums, records, and (dependent) pattern matching in Agda only work well when being top-level bindings. [agda-bad-bad]: https://github.com/agda/cubical/pull/57#discussion_r253974409 [agda-bad]: https://github.com/agda/agda/issues/1209 ## Features + First-class language components + Sum/Record + Dependent type goodies + Pi/Sigma ### Extensible ADTs Voile supports sum-types (coproduct), record-types (product) and their instances as first-class language components. First-class record support is related to [Record Calculus][rec-calc], or [Extensible Records][ext-rec], or "first-class labels". The idea of "extensible record" is that the creation, manipulation and destruction of "records" can be done locally as an expression, without the need of declaring a record type globally, like: $$ \newcommand{\Bool}[0]{(\texttt{True}\mid\texttt{False})} \begin{alignedat}{2} &\texttt{not}&&:\Bool \rarr \Bool \\\\ \space &\texttt{ifThenElse}&&:\forall A. \Bool \rarr A \rarr A \rarr A \end{alignedat} $$ Universal quantification should also support generalizing over a part of the records (in other words, [row-polymorphism][row-poly]), like: $$ \newcommand{\xx}[0]{\texttt{X}} \newcommand{\T}[0]{\lBrace\xx:A, ...=r\rBrace} \begin{alignedat}{2} &\texttt{getX}&&:\forall A. \T \rarr A \\\\ \space &\texttt{getX}&&=\lambda s. (s.\xx) \\\\ \space &\texttt{setX}&&:\forall A. \T \rarr A \rarr \T \\\\ \space &\texttt{setX}&&= [\textnormal{syntax undecided yet}] \end{alignedat} $$ Existing row-polymorphism implementation divides into two groups according to how they support such generalization, either by making "record type"/"record value" first-class expressions, or by introducing a standalone "row" (the type of $r$ above) type. The study on extensible records has a long history, but there isn't much research and implementations on extensible sums and the combination of bidirectional type-checking and row-polymorphism yet. <br/> Currently, I can only find one programming language, [MLPolyR] (there's a [language spec][spec], a paper [first-class cases][fc-c], a PhD thesis [type-safe extensible programming][tse] and an [IntelliJ plugin][ij-dtlc]), whose pattern matching is first-class (in the papers it's called "first-class cases"). First-class pattern matching is useful because it solves the expression for free, which means that library authors using such languages can split their library features into several sub-libraries -- one core library with many extensions. Library users can combine the core with extensions they want like a Jigsaw and exclude everything else (to avoid unwanted dependencies) or create their own extensions without touching the original codebase. [rec-calc]: https://dl.acm.org/citation.cfm?id=218572 [ext-rec]: https://wiki.haskell.org/Extensible_record [row-poly]: https://en.wikipedia.org/wiki/Row_polymorphism [MLPolyR]: https://github.com/owo-lang/mlpolyr [fc-c]: https://people.cs.uchicago.edu/~blume/papers/icfp06.pdf [tse]: https://arxiv.org/abs/0910.2654 [spec]: https://people.cs.uchicago.edu/~blume/classes/spr2005/cmsc22620/docs/langspec.pdf [ij-dtlc]: https://github.com/owo-lang/intellij-dtlc ### Exceptions (undecided yet) MLPolyR exploits first-class sums in error-handling -- exceptions are treated as first-class sums while `try`-`catch` clauses are pattern matching on them ("consumes" a variant in a sum). Putting exceptions into function signatures looks like Java's `checked exceptions`, but with full type-inference. In this way, we can have cross-control-flow exceptions (instead of monadic) safely, because it's easy to ensure that an expression is exception-free simply by looking at its type. We can denote function from $A$ to $B$ that may throw exception $E$ like this: $$ A \xrightarrow{E} B $$ A higher-order function taking an exception-throwing function and handles one exception will have signature like this (convert langauge-level exceptions to monadic exceptions): $$ (A \xrightarrow{E \mid r} B) \rarr (E \rarr B) \rarr (A \xrightarrow{r} B) $$ However, without the help of dependent types, there can be false positives such as conditionally-thrown exceptions -- consider a function `f` like this (assume $e : E$): ```mlpolyr fun f a = if a then throw e else 0 ``` Invocation `f false` is not going to raise any exception, but the compiler disagrees because of the type of `f` inferred (something like $\mathbb{B} \xrightarrow{E} \mathbb{Z}$) is irrelevant to the argument applied. In the industry of dependent types, there isn't much development on exceptions. We might have a try here. ### Induction and Coinduction According to elementary-school discrete math, induction has something to do with recursion. However, recursion on sum types is a huge problem against the design of first-class sum types. In the cliché programming languages with non-first-class sums (where the sum types need to be declared globally before usage), type-checking against recursive sums can be easily supported because the types are known to the type-checker -- there's no need of reduction on an already-resolved sum type. Once a term is known to be some sum type, it becomes a canonical value. For Voile, arbitrary expressions can appear inside of a sum type term, which means reduction is still needed before checking some other terms against this sum-type-term. If there's recursion on a sum-type-term, like the natural number definition: $$ \mathbb{N}=\texttt{Zero} \mid \texttt{Suc}\ \mathbb{N} $$ The type-checker will infinitely loop on its reduction. The above definition will actually be rejected by the termination checker, but recursion on sum-types *have* to be supported because we have been using it for a long time -- we shouldn't sacrifice this fundamental language feature. We choose to annotate types with the so-called sized types (present in [MiniAgda]) to inform the compiler about how data size are changed in a function. This will also help recursive type definitions, because it acts as an argument to the recursive call in the type definition! $$ \mathbb{N}^{(\texttt{s}\ i)}=\texttt{Zero} \mid \texttt{Suc}\ \mathbb{N}^i $$ This function now perfectly terminates. We may also write it in a more inductive way: $$ \begin{alignedat}{2} &\mathbb{N}^0&&=\texttt{Zero}\\\\ \space &\mathbb{N}^{(\texttt{s}\ i)}&&=\texttt{Suc}\ \mathbb{N}^i \end{alignedat} $$ Depends on how sized types are designed in Voile. # Implementation Voile's implementation is inspired from [Agda], [mlang], [MiniAgda] and its prototype, [minitt]. [MiniAgda] supports induction, coinduction with sized types. <p style="color: yellowgreen;"> TODO Something needs to be written here. </span> [Agda]: http://www.cse.chalmers.se/~ulfn/papers/thesis.pdf [MiniAgda]: http://www.cse.chalmers.se/~abela/miniagda [mlang]: https://github.com/molikto/mlang [minitt]: https://lib.rs/crates/minitt <br/> <span> <details> <summary>About the name, Voile</summary> <span> This name is inspired from a friend whose username is <a href="https://www.codewars.com/users/Voile"><em>Voile</em></a> (or <a href="https://github.com/Voileexperiments"><em>Voileexperiments</em></a>). However, this is also the name of a library in the <a href="https://en.touhouwiki.net/wiki/Scarlet_Devil_Mansion"><em> Scarlet Devil Mansion</em></a>. </span></span> <span><details> <summary>The librarian of Voile, the Magic Library</summary> <img src= "https://raw.githubusercontent.com/owo-lang/voile-rs/master/rustdoc/voile-librarian.png" alt="" /> </details> </details></span> */ /// Abstract syntax, surface syntax, /// parser and well-typed terms (core language). pub mod syntax; /// Type-Checking module. pub mod check;